Rewrite as a simplified fraction. ${0.1\overline{58} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 158.5858...\\ 10x &= 1.5858...\end{align*}}$ Subtracting the two equations, we have: ${990x = 157}$ ${x = \dfrac{157}{990}} $